Rolling bones and other things

[JSDiamond]

This was brought up by james_west and got me to thinking.  How does the physical system-mechanic of a game affect its 'feel'?

I chose percentiles (2d10) for Orbit for this reason: Many console rpgs use this mechanic (Final Fantasy, Lunar, Suikoden). Without reading the rules it's easy to see how able your character is at any number of tasks.  Now, I am not a big fan of those games, so my 'instant understanding and awareness' of the system (while only half-paying attention while my wife played Lunar) conveyed to me something *very* important:  

1. I immediately identified and recognized the mechanics of it while hardly watching.
2. Everyone already  understands a 'percentage chance' of success.
3. Orbit's system will therefor be 'invisible' while the characters and setting will be the star.

Perfect!
Anyway, that's my spin.

Now, on the other hand, the mechanics of a game can also bring the game to life by sharing that spotlight. Poker chips for Deadlands is a great example because it puts a common western prop (chips from a saloon card game) right into your hands.  There's a connectivity; the gambler plays with chips while playing cards in the Red Garter Saloon, and I have a few of them right here.    

So 'why' did you choose your game's resolution mechanic? And by 'resolution mechanic' I mean both the physical tools plus the system. Did it have anything to do with the feel of the game, or was it mainly a matter of (desired) simplicity or complexity?

Jeff
           

[Dav]

Um, we chose ours because it was simple (relatively) while still giving myriad possibilities of outcome.  For those not familiar with it, Obsidian uses a d6 mechanic loosely based off of the old Star Wars system... or so I've been told.

But, in theory, it gave the desired complexity of outcome with a relatively simple input.  In this case, I think your goal and my own are similar.

Dav

[Ron Edwards]

Sorcerer was specifically built to create universal uncertainty about the outcome of conflict, most particularly interpersonal (sorcerer & demon) conflict.

That's why it's built on roll vs. roll, with the high value winning (not total, but single value). Every conflict in Sorcerer is resolved this way: physical, social, or magical. The fellow with the low number of dice always has a chance. The fellow with the high number of dice is never sure.

Is that demon going to betray me?
Is that guy going to kick my ass?
Is my loved-one going to believe me?

The game is about uncertainty for everyone, and most particularly forcing the GM to know that he or she must be ready for ANY outcome of ANY conflict. This is not a game about moving from obstacle to obstacle - it's a web of ever-proliferating possibilities.

The dice themselves were chosen for speed. Without target numbers, and without any modifiers except adding or subtracting dice, this highest-value system is faster than any Fortune method I have encountered.

Best,
Ron

[Mike Holmes]

Yep, that Sorcerer fortune method is pretty slick. Glad I invented it.

I came up with that years ago, but thought that it might be impractical. Then I incorporated it into my spreadsheet system and it works like a charm. To be exact, my system divides the stat in question by three (retaining fractions) and then generates three random numbers from 0.000 to that figure. Thus you always have the classic bell curve for all roles, and always a possibility of rolling from 0 to the stat in question with the average result being exactly half. So any roll can beat any other, it's just very unlikely in some cases.

I really have gotten behind the all opposed rolls methods of late. It is not any slower, as you point out, and it has all sorts of other advantages, including that you always have a chance to win without using open-ended die rolling systems which are usually clunky and flawed. I find it interesting that most people like to divide up opposed and non-opposed rolls between active and passive opponents/tasks. This seems intuitive, but nobody has given me a reason why the math makes any more sense.

Mike Holmes

[J B Bell]

Well, this topic is pretty old, but no sense starting a new one.

I got here from reading the excellent Sorcerer archives, where Ron defined a few different dice fortune systems:

1. Flat, separate damage (or, presumably other outcome variable) roll
2. Flat, incorporated damage
3. Bell curve, separate damage
4. Bell curve, incorporated damage

Sorcerer is, of course, of type 4.  And, I should add, it has the most kickass dice resolution I think I've ever seen.  (Ron also complained in the archive of people not noticing this.  Not to worry Ron, once I finish up a few sessions, I'll be posting to RPG.net with suitable lauds for it.)

I'm a FUDGE refugee.  FUDGE is nifty for Gamist/Sim types, and it turns out I've got
a powerful Narrativist bent & didn't know it.  Much GMing woe could have been avoided, but oh well.  The thing is, FUDGE people love, love, love to come up with alternate dicing mechanics, because it has a couple of misfeatures that greatly exacerbate whiff syndrome:  first, you use four dice, producing a nice bell curve, but, second, the granularity of results is low.  And, making most combat rolls opposed makes things wildly variable over that small set of results (for the record, running from -4 to +4, though basically doubled to -8 to +8 for opposed rolls).

"Highest die wins, no target number but other dice" allows low skills to beat not just higher skills, but arbitrarily higher skills, with increasingly vanishingly tiny chances.  But chances nonetheless.  While this system lacks an explicit critical system (well, having all of my dice turn up higher than any of yours is called Total Victory, and has a Nifty Factor that is left up to the GM), it's easy to add such if you want and make sure that the skinny ends of its bell curve disappear asymptotically.  (There's a special rule too, that says if a single-die opponent or difficulty ties the highest value of a larger number of dice, it's a win for the party with the bigger number of dice--but not a big win.  So serious disparities still turn out about right--once you get to five dice or more, unless you're talking d100, your chances of rolling a couple maxes are pretty darned good.)

Honestly, this is one of the Holy Grails of dice mechanics.  For me, anyway.  The only people it would make unhappy would be, IMHO, the most humorless variety of Simulationists.

OK, all obeisance to the Cult of Ron aside, there is one thing that still gripes at my Gamist heart (the spare that I keep on my desk)--just how much does an x die penalty affect a roll of this kind?  Because, a big problem with FUDGE and other bell-curve systems is that +1 means something different to a guy with a skill of, say 11 (if we're trying to get that or less on 3d6) as opposed to 16.  To be really math-geeky, looking at your bell-curve, the change in x, the roll modifier, is not proportional to the change in y, the percentage chance of hitting a certain roll.  I think those wacky guys at Blacksburg Tactical Research Center actually tried to handle this with an ungainly chart in Warp World, but I'm not sure.

I want charts damnit!  I'm sorry.  I can't help it.  The guys on the FUDGE list crank them out an hour after they're requested.  But they're just using an additive system.  I'll happily provide folks with code to make these kinds of rolls in Python, but I'm no whiz at making histograms or that sort of thing.

Ron?  Was this a leap of faith for you, or are you sitting on yellowed, ancient scrolls from the Han dynasty that nicely plot this out?  I know you wanted uncertainty, but I'm a constitutional GM, and you know about the control-freak thing--my players don't care, but I gotta have the variables, man.  *Choke*  I gotta.  I need my stuff!  And don't tell me you don't want an Origins award for "Most Kickass Fortune Mechanic for G, N, or S-style Systems."

OK, I'll go take my meds now.

--TQuid

[Mike Holmes]

Honestly, this is one of the Holy Grails of dice mechanics.  For me, anyway.  The only people it would make unhappy would be, IMHO, the most humorless variety of Simulationists.

Why would they be disapointed? I think the system could be applied to hardcore Sim. If you need finer granularity just double or tripple the stats, a voila, instant granularity shift.

... there is one thing that still gripes at my Gamist heart (the spare that I keep on my desk)--just how much does an x die penalty affect a roll of this kind?  Because, a big problem with FUDGE and other bell-curve systems is that +1 means something different to a guy with a skill of, say 11 (if we're trying to get that or less on 3d6) as opposed to 16.  To be really math-geeky, looking at your bell-curve, the change in x, the roll modifier, is not proportional to the change in y, the percentage chance of hitting a certain roll.  I think those wacky guys at Blacksburg Tactical Research Center actually tried to handle this with an ungainly chart in Warp World, but I'm not sure.

Do I have it right that your problem is that a modifier in these systems modifies by a different amount for people of varying abilities? Assuming that's what you mean, I see this as a feature, not a problem. Most advantages in resolving a problem in RL do have a diminishing return. If you look at actual studies of how much better people perform in one circumstance than another, there is a tendency to make an erroneous assumption. That is, if on circumstance A I have a 60% chance of doing something right, and in circumstance B I have a 80% chance, most people will assume that the differentiating variable gives me a +20% chance to accomplish that task. But this is nonsense. If I had a 90% chance of success would that same advantage make me 100% successful (can't be 110% successful)? No, testing will show that it probably raises me to 95% or so. Or rather, my chance of faiure is reduced by 50%. This is the very natualistic diminishing return in effect. Or for other math geeks out there, the effect modifies the margin. Anyhow, Ron's system and others like it, simulate these sorts of curves very well.

I want charts damnit!  I'm sorry.  I can't help it.  The guys on the FUDGE list crank them out an hour after they're requested.  But they're just using an additive system.  I'll happily provide folks with code to make these kinds of rolls in Python, but I'm no whiz at making histograms or that sort of thing.

As you can see, not at all neccessary. The people who have done the most investgaton into how these things work are, not surprisingly, the GURPS folks. Do you think having a guy with a physics PhD as your line editor might have that effect (luv ya Kromm!) If you go over to their sites (www.SJGames.com, or IO.com) you can find a lot of people who have worked these things out.

Note that dice pool systems in general were a response to the GURPS problem that their curve has a limited range, and not the nice assymptotic tails that, say, Ron's system has. Here's a method that I'm using for a game that I'm developing for those that don't mind addition and subtraction but like as few a dice as possible (each player needs only one):

All opposed rolls. Each opponent rolls skills/stats/modifiers, whatever, plus a D10. Rolls of ten explode and roll again, ad infinitum. High roller scores successes equal to the difference. Simple.

Since there are only two dice, the curve is actually a pyramid (with walls that slope less and less asymptotically), not a bell, but that's not totally unrealistic either, and produces rather adventurous results, IMO.

Mike

[Le Joueur]

Ron defined a few different dice fortune systems:

[list=1][*]Flat, separate damage (or, presumably other outcome variable) roll
[*]Flat, incorporated damage
[*]Bell curve, separate damage
[*]Bell curve, incorporated damage[/list:o]Sorcerer is, of course, of type 4.

There are (using the above methodology, at least two more:

[*]Sigmoid, separate damage
[*]Sigmoid, incorporated damage[/list:u]Sigmoid graphs (they look like a lazy ‘S’ leaning over to one side) appear when your using one of the familiar ‘multiple dice, sum is less than or equal to target number’ mechanics.  Even using two dice, which has an angular (it looks like the silhouette of a pyramid) distribution, becomes a smooth sigmoid when you use a ‘less than or equal’ approach.  (We chose type 6 for Scattershot. <-- that's actually five links)

As an example, in Scattershot, you roll two ten-sided dice and subtract that from your modified rating (target number).  Any non-negative result is success (then you apply the rest of the FitM mechanic to the value generated which "incorporates" the effect, but I won’t go into that here).  Now with the sum of two ten-sided dice (having exactly one hundred potential outcomes), it is pretty easy to calculate the percentage chance of any total.  There’s 1% chance of rolling a 2, 2% of 3, 3% of 4, and so on linearly up to 10% of rolling an 11; then the curve goes right back down, just as linear, to 2% of rolling a 20.  Not too ‘bell shaped’ or smooth of a ‘curve.’

It becomes smooth when you realize that a success is any roll less than or equal to the target number.  For example, to roll 5 or less is 1% + 2% + 3% + 4% or 10% (see the graph below).

Honestly, this is one of the Holy Grails of dice mechanics.  For me, anyway.

You weren’t clear on which Grail was the one you wanted.  Can you please clarify?

There is one thing that still gripes at my Gamist heart -- just how much does an x die penalty affect a roll of this kind?  Because, a big problem with FUDGE and other bell-curve systems is that +1 means something different to a guy with a skill of, say 11 (if we're trying to get that or less on 3d6) as opposed to 16.  To be really math-geeky, looking at your bell-curve, the change in x, the roll modifier, is not proportional to the change in y, the percentage chance of hitting a certain roll.

"There are points wherein new circumstances will fail to have any impact on a given situation. When shooting fish in a barrel, to use an extreme example, the addition of a sniper scope just doesn't make things easier." -- Larry D. Hols

The problem is should the ‘change’ be proportional between modifier and percentage chance?  I’d have to argue it shouldn’t be, but that would only be my opinion, so I won’t go into detail.

I want charts damnit!

but I'm no whiz at making histograms or that sort of thing.

Okay, how about this one:

Code Select Expand

Sum of Two Ten-sided Dice versus Target Number

100                                               ,,,,gggaaa
90                                        ,,gdY"""’’
80                                   ,,,gd""’
70                               ,,dP"’
60                            ,dP’
50                          ,8’
40                      ,dP"
30                  ,,dP"’
20             ,,gdP"’
10  __,,,aaadP""’
    2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
^%^                     Target Number
This isn’t so much about just being ‘diminishing returns,’ but more about what Mr. Hols is quoted for.  The reason I prefer these is so that when characters have a great deal going for them (lots of modifiers in their favor), I just don’t see how they can have better than a 100% chance.  (But even then Scattershot uses a Critical Juncture Threshold to mitigate them having too much in their favor, anyway.)

Fang Langford

[Ron Edwards]

Agreed on adding the sigmoid issue, Fang. Good call. My original thoughts on this were along the lines of "flat vs. curve-of-any-sort," but I did write "bell," now didn't I? Thus I stand corrected.

Another point worth reflecting on is that a "separate effect" can have a variety of curve/lines itself ...

Thus:
Flat, bell, sigmoid (all w/incorporated effect)
Flat, bell, sigmoid (all w/separated effect)
... and as a subset of the above line, for each of the three
... Separated effect (flat, bell, sigmoid)

That gives us (let me see) 3 + (3*3) outcomes = 12 types. Oich.

Best,
Ron

[efindel]

One of my favorite dice mechanics that I've seen is from the game Don't Look Back.  It works like this:

Add up all the modifiers to your check.  This includes skill, any bonuses from attributes, situational modifiers, etc.  This gives you a number that's generally going to be in the range of -5 to +5.

Roll a number of d6 equal to the absolute value of the modifier plus 3.

If your total modifier was negative, take the lowest three dice.  If the total modifier was positive, take the highest three.  (And, of course, if the modifier was zero, take the three you have.)  The total of those dice is your result.

There's a little table for interpreting results, but basically 12+ is success, 9- is failure, further up/down gives better/worse results.  10-11 is partial success, partial failure.

The thing I really like about this mechanic is that the possible range of results is fixed -- even if you have a -8 modifier, it's still *possible* for you to get an 18 result.  It's just very, very unlikely.

[Mike Holmes]

That gives us (let me see) 3 + (3*3) outcomes = 12 types. Oich.

Oh c'mon, guys. Thre are obviously an unlimited number of types. Not all as usefull a others, but then some of the twelve are probably more usefull than others as well.

Mike

[J B Bell]

Why would [Simulationists] be disapointed [with a Sorcerer-style dice pool]? I think the system could be applied to hardcore Sim. If you need finer granularity just double or tripple the stats, a voila, instant granularity shift.

I agree it would work for hard-core sim.  I'm thinking specifically of a thread on the FUDGE list regarding Gawain the knight, and how a peasant should never, period, be able to sucker-punch him, if one is simulating the genre of Arthurian legend.  On reflection, this guy wanted the system to answer a literary constraint that might more be a Narrativist concern than strictly Simulationist.  Nonetheless, the Simulationist way, too, would be to simply say "after a certain skill divergence, or given Legendary Plot Immunity, mooks cannot hit you."  Or use a non-asymptotic curve.

My apologies if I inadvertently besmirched Simulationism; this was not my intention.  I wrote my post late at night and without adequate adult supervision.

... there is one thing that still gripes at my Gamist heart (the spare that I keep on my desk)--just how much does an x die penalty affect a roll of this kind?  Because, a big problem with FUDGE and other bell-curve systems is that +1 means something different to a guy with a skill of, say 11 (if we're trying to get that or less on 3d6) as opposed to 16.  [Change in x on the bell curve does not equal change in y]

Do I have it right that your problem is that a modifier in these systems modifies by a different amount for people of varying abilities? Assuming that's what you mean, I see this as a feature, not a problem.

You're right, and I mis-stated what my problem is.  The problem I have had historically with bell-curve dice systems in skill-based systems, such as GURPS, is that they are "opaque".  That is, doing the math is difficult because there's a price curve on higher skill levels, and yet there's another curve to deal with in the fortune system.  Diminishing returns is a fine thing, but doubling up the diminishment leaves the Gamist in me feeling he's getting taken for a ride somewhere.  The math for the skill-cost curve isn't hard at all, and neither is the math for "roll x or less on 3d6", but figuring the two together is, well, I have no idea how to do it.

This irritation led me to the notion of "transparency" as being a virtue in a game; I now see that this ain't necessarily so, depending on what kind of information control you want in your game.  But I do still think "Put Your Curve in One Place" is a good design principle, or at least one that attracts me as a player & GM.  So if you have a curve in skill cost, use a flat fortune system.

Another reason I've converted to liking dice pools is that the diminishing return itself is easy to do the math on.  If each die represents a certain % chance of success, adding another gives me an "and", probabilistically speaking, and that math is easy.  "I need a 7 or better to succeed.  If I have one die and I add one, that's like adding 30% of 30%, so I go up to 40%."  I don't actually do that math in play, but knowing what the math is gives me a nice, intuitive grasp of the diminishing return.

This, BTW, is the Holy Grail I meant:  an asymptotically curved system with relatively easy-to-understand diminishment.  Really ideally, I'd like something that uses d6, too, which Ron's system can, but it doesn't get granularity I like until you get to d10 (the one other kind of die I care for, with some grudging acceptance of d20).  This is what you get when you sit alone in your apartment trying to figure out the "perfect" fortune system without reference to, you know, an actual game.

Note that dice pool systems in general were a response to the GURPS problem that their curve has a limited range, and not the nice assymptotic tails that, say, Ron's system has. Here's a method that I'm using for a game that I'm developing for those that don't mind addition and subtraction but like as few a dice as possible (each player needs only one):

All opposed rolls. Each opponent rolls skills/stats/modifiers, whatever, plus a D10. Rolls of ten explode and roll again, ad infinitum. High roller scores successes equal to the difference. Simple.

Since there are only two dice, the curve is actually a pyramid (with walls that slope less and less asymptotically), not a bell, but that's not totally unrealistic either, and produces rather adventurous results, IMO.

Oh, that's quite nice, and demonstrates the power of pool systems in a different way--open-ended additive systems can get quite ridiculous, apparently (never used 'em myself), but since you're adding "successes" instead of ending up with a "300% success", it's a little easier to interpret.  And you don't need big fistfuls of dice either.  Kudos.

--TQuid

[Jack Spencer Jr]

So 'why' did you choose your game's resolution mechanic? And by 'resolution mechanic' I mean both the physical tools plus the system. Did it have anything to do with the feel of the game, or was it mainly a matter of (desired) simplicity or complexity?

Well, for The Wheel  I've been struggling rather mightily with a few odd concepts that have all come to me at the same time.

I wanted to do away with numerical stats, mostly to see if I could make it work. I had my doubts, but most game that claim to do away with numbers (i.e. The Window, FUDGE) actually do use numbers after all, no matter how they try to hide them.  

Those that don't I've noticed requiring the player to write an essay, 50 words seems to be average, about their character.  I didn't like this idea since numbers give you an easy shorthand, so we do away with numbers to gain a 50 word essay??  I wanted an easy short hand that didn't use numbers.

I had been toying with the idea of character classes, while not a fixed set of classes but a user defined "class" of some kind, but I was having trouble figuring out exactly what I was aiming for.  Then I read From The Land of Fear by Harlan Ellison which contains a few unfinished fragments.  One of these is titled One / Word / People and deals with how some people can one word that can explain an awful lot about them.

This melted away most of my problems with my own concept.  One word that sums up your character.  

From here my idea gets weird.

Most games have the system as something that must be overcome, either through good dice rolling or high enough stats so that the odds are in the player's favor.  I wanted to try to get away from this and simply have the character do what the player wants.  At the same time, I hope to encourage the player to want for something other than inequivical success for their character.  They have to want their character to fail sometimes, as it would make a good story.

I haven't tried to make any story making mechanics since I don't personally believe that any contivance I could make could compare to the sense of story of a living human mind.  Besides, this would mean that I would make yet another system that could need to be overcome in a certain situation.  Therefore, I decided to let the player's yes be yes and no be no and move on.

Now, to keep the game from simply being round-robin storytelling, I borrowed a page from Wallis's Baron Munchausen and expanded it a bit.  Tokens purchase the other players the right to alter the first player's story in various ways.  Changing an event, playing an NPC, introducing their own PC, etc.

This means that the main random factor is not a die but the other player's sense of story.  As they interact with the scene, they will effect changes to the first player's origial plan, hopefuly with beneficial results.  ;)

There is another random factor in the Inspiration Deck which is supposed to have fairly vague statements or sayings on them a la the I-Ching or the meanings of Tarot cards or something similar.  

One use for this deck is for the player if he should get completely stuck.  I got this idea from the Edgar Wallace Plot WHeel mentioned in the present text.  (Interesting side note:  The Edgar Wallace society, run by his granddaughter, has never heard of the Plot Wheel.)

Another use is to have the players each draw a card at the begining of the session.  This gives them a random idea to try to work into their scene when it becomes their turn.

Since this thread is about resolution mechanics, and I've covered that and more, I leave it here except to mention that I had a dice mechanic in The Wheel which is still in the present document.  But I've since decided to ditch it since all of the above already covers everything, so there is no need for the dice.  I put it in in the first place because when I started I was doggedly determined to use dice in the game.  But after a while, I've decided against it.  See how a plan can go awry?

[Bailywolf]

I'm sorry if this post is a bit of thread hijack, but it raised some questions for me about a mechanic I've been toying with... and since everyone is focused on mechanic and statistics, let me hit you with it... it seems neat... but I have no idea if it holds up.

characters are rated based on their abilities in campaign specific areas of conflict.  In everything else, they are as good as the player wants them to be because they have no effect on the game's central conflict.  Martial, Magical, Social, Practical, Mental... etc.  

Characters are defined by assigning a pool of points to the thee elements of each arena.  If the characters are intended to be powerful, and there are three importiant arenas in the game, they might be granted 13/10/8 to assign.

The easiest to describe is based on phsycial combat.  Each arena has three elements which describe it.  For martial they are:

Might- how powerful are your moves (acts as a die cap, rated 1-6)

Finess- How skilled are you (how many dice can you throw per bout 1-6)

Techinque- what you know how to do (free techniques are Attack, Defense, and Initiative.  there are others, but they are outside the basic mechanic I'm describing).

You roll your finess, round down any dice showing values greater than your Might, then assign them to Techniques.  Assign Attacks, reveal attack in reverse initiative order, then assign defenses.  Defense values counter attacks highest to lowest (other techniques allow a player to monkey with this after the fact).

Multiple dice can be assigned to each technique.

Some complications:

Gimmies-  these are free values assigned to certain techniques.  Everyone has a single free gimmie of "1" in each basic technique.

Lumps- specialized characters can add the value of one or more dice (after rounding down to might level) up to no more than twice their Might rating.

Raises- specialy focused characters have their might increased in certain circumstances.

Takes- in some circumstances, Might is reduced for specific techniques. (example is armor.  it grants a Gimmie to defense but inflicts a Take to initiative, both getting more significant as the armor gets heavier).


Damage- based on margine of success (attack vs defense) multipled by weapon damage factor.  Characters can take as much damage as they have points assigned to the arena.



Now my question... how the hell do I figure out the odds on this?  

I was going for a very tactile system.  Roll the dice, then move them around on your character sheet lining them up alongside the technique you want to use, stacking them for Lumps, flipping them down when they get capped by Might or a Take.  

My only statistic class is long since gone into the murks of time... so so sad...


Thanks all



Benjamin

[Mike Holmes]

Benjamin,

First, there were a few ambiguous things in your post. Like the number of sides on the dice (I assume six?). But I think I get it in general.

Due to the takes and might caps, the formula for what fractional chance you have to roll a particular damage when comparing an attack of a certain might vs. a defense of a certain might is very complicated. How important is it?

I like the idea of the system somewhat. I've always thought that it would be interesting to look at effectiveness distribution from the POV of what the game is about. Too often wine tasting costs as much as Starship Piloting, which doesn't balance in terms of protagonism.

Mike

[Bailywolf]

Mike, thanks for the response.

Yup.  Good old six siders.  I'd just as soon use them for everything.  They have so much charm.

Another desingn consideration is actualy making the rolling and aranging kinda fun in and of itself even beyond the utility of an RPG resolution mechanic.  Instead of sequestering dice off, I wanted to system which could be enjoyed on several lebels- tactile (rolling the bones), tactical (aranging and using special abilities to wiggle them around), and persona (actualy playing the chaarcter).

In terms of how the rules and setting interface, I figured anything not directly related to the setting's central conflict doesn't matter, so players can make it anything they want.

For a game of waring wizards bent on political and magical hijinks, the arenas would be :

Magic
Politics (or Social, or some such)

Beyond this, wizards can be masters at any mundane skills they want... but Magic and Politics dwarf everything else in importiance.  The rest can be covered in a good description and backstory.

For a traditional fantasy setting, this might be better:

Each character selects 4 Arenas to be rated in, distributiung 14/12/10/8

Martial
Magical
Social
Survival
Thievery
Practical

For a Kung Fu game:

Martial
(and perhaps) Social.

For a certain SciFi setting:

Martial
Piloting
Force
Survival
Technology
Social
Practical
Shady